Many color images use 24 bits for color information. However, this number of colors is not always necessary. In this paper, an algorithm that quantizes a full-color image from about 17 million to 256 colors is proposed. The quantized colors are calculated so that the sum of squared quantization errors is minimized. To quantize the color image, the fast K-means algorithm is proposed. This algorithm classifies K clusters into groups. These groups are used to decrease the number of calculations and the execution time. The fast K-means algorithm is effective when K is large. The results show that for K = 256 the execution time is less than a quarter of that for the K-means algorithm. © 2000 Scripta Technica, Syst Comp Jpn, 31(8): 33–40, 2000